= Planck normalization of a cubic curvature interaction
{c}
{title2=$H_{\mathrm{int}}\propto M_{\mathrm{Pl}}^2a^3\epsilon^2\zeta\dot\zeta^2$}
The <comoving curvature perturbation> is dimensionless. With spatial coordinates and time carrying inverse mass dimensions, the cubic interaction $\int dt\,d^3x\,a^3\epsilon^2\zeta\dot\zeta^2$ needs a mass-squared coefficient. Its standard gravitational normalization is $M_{\mathrm{Pl}}^2$. Six <De Sitter curvature mode functions> supply $M_{\mathrm{Pl}}^{-6}$; this vertex then supplies $M_{\mathrm{Pl}}^2$, leaving the physical $M_{\mathrm{Pl}}^{-4}$ curvature <primordial bispectrum>. The <Wick-pairing multiplicity for a zeta zeta-prime-squared vertex> is independently six: three choices of undifferentiated external leg times two differentiated-leg assignments.
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